```Date: Feb 15, 2005 4:48 PM
Author: Guess who
Subject: Re: Max. Income, Quadratic Equation

On Tue, 15 Feb 2005 04:49:05 GMT, "Darrell" <dr6583@comcastsnip.net>wrote:>>> A plane with 100 seats may be chartered for \$200 per person plus a fee>>> of \$5 per person for each empty seat. What number of passengers will>>> provide the maximum income?>> Let p be the number of passengers and i the income then>>>> i = p*200 + p*(100 - p)*5>>  = 700*p - 5p^2>>>> and you need to maximize i.  Note that it makes no sense to>> differentiate i wrt p because neither is a continuous variable.>>That doesn't matter; for all intents and purposes the problem can be >modelled by this (continuous) function. Agreed.  Any problem in misunderstanding can be avoided if algebra[completing the square] is used instead in this instance.-- submissions: post to k12.ed.math or e-mail to k12math@k12groups.orgprivate e-mail to the k12.ed.math moderator: kem-moderator@k12groups.orgnewsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html
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